What are the first three terms of an arithmetc series in which a1=9

ań=105 and sn=741

to find n, just solve

n/2 (9+105) = 741

Now find d, using

9+(n-1)d = 105

Why did the arithmetic series bring a1 with it to the party? Because a1 is the first term and it didn't want to show up empty-handed!

Now, let's find the common difference, shall we? We know that a1 = 9, an = 105, and the sum of the series (sn) = 741.

The formula for the sum of an arithmetic series is:

sn = (n/2) * (2a1 + (n-1)d),

where n is the number of terms and d is the common difference.

Now, we can use this formula to find the common difference:

741 = (n/2) * (2 * 9 + (n-1)d).

We can simplify this equation to:

741 = (n/2) * (18 + (n-1)d).

Divide both sides by (n/2):

741 / (n/2) = 18 + (n-1)d.

Multiply both sides by 2/n to get rid of the fraction:

1482/n = 18 + (n-1)d.

Now, let's solve for d. Since the problem gives us a1 = 9, we can substitute that in as well:

105 = 9 + (n-1)d.

Subtract 9 from both sides:

96 = (n-1)d.

Divide both sides by (n-1):

96 / (n-1) = d.

Now we know the common difference! Let's plug that back into the equation to find the first three terms, starting with a1 = 9:

a2 = a1 + d
= 9 + (96 / (n-1)).

a3 = a1 + 2d
= 9 + 2 * (96 / (n-1)).

There you have it! The first three terms of the arithmetic series are a1 = 9, a2 = 9 + (96 / (n-1)), and a3 = 9 + 2 * (96 / (n-1)). Keep in mind that you'll need to substitute the value of n into the equations to get the actual terms.

To find the first three terms of an arithmetic series, we need to use the formulas for the nth term (an) and the sum of the first n terms (Sn).

Given information:
a1 = 9 (first term)
an = 105 (n-th term)
Sn = 741 (sum of the first n terms)

Step 1: Find the common difference (d).
Using the formula for an = a1 + (n - 1)d, we can plug in the given values:
105 = 9 + (n - 1)d

Step 2: Find the value of n.
We are given that Sn = 741. Using the formula Sn = (n/2)(a1 + an), we can substitute the known values:
741 = (n/2)(9 + 105)

Step 3: Solve for d and n using the two equations from Step 1 and Step 2.

Step 1 (continued):
105 = 9 + nd - d
96 = (n - 1)d
d = 96 / (n - 1)

Step 2 (continued):
741 = (n/2)(9 + 105)
741 = (n/2)(114)
2 * 741 = n * 114
1482 = 114n
n ≈ 13

Step 3: Substitute the value of n into the equation for d:
d = 96 / (n - 1)
d = 96 / (13 - 1)
d = 96 / 12
d = 8

Step 4: Find the first three terms using the formula an = a1 + (n - 1)d.

a2 = a1 + d
a2 = 9 + 8
a2 = 17

a3 = a1 + 2d
a3 = 9 + 2(8)
a3 = 9 + 16
a3 = 25

Therefore, the first three terms of the arithmetic series are: 9, 17, 25.

To find the first three terms of an arithmetic series, we need to use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

Where:
an = nth term of the arithmetic sequence,
a1 = first term of the arithmetic sequence,
n = term number,
d = common difference between terms.

Given:
a1 = 9
an = 105
sn = 741

Let's start by finding the common difference (d). We can use the formula for the sum of an arithmetic series (Sn):

Sn = (n/2)(a1 + an)

We are given that Sn is 741, so we can set up the equation:

741 = (n/2)(9 + 105)

Now, let's solve for n:

741 = (n/2)(114)
741 = 57n
n = 741/57
n ≈ 13

Therefore, the term number (n) is approximately 13.

Now that we have the value of n, we can find the common difference (d):

d = (an - a1)/(n - 1)
d = (105 - 9)/(13 - 1)
d = 96/12
d = 8

Now, we have the common difference (d), and we know that the first term (a1) is 9. We can use the formula for the nth term to find the terms:

a2 = a1 + (2 - 1)d
a2 = 9 + (2 - 1)8
a2 = 17

a3 = a1 + (3 - 1)d
a3 = 9 + (3 - 1)8
a3 = 25

Therefore, the first three terms of the arithmetic series are:
a1 = 9
a2 = 17
a3 = 25